Embibe Experts Solutions for Chapter: Statistics, Exercise 1: KEAM 2018

In an examination, $20\%$ of the students scored $70$ marks, $40\%$ scored $80$ marks, $30\%$ scored $90$ marks and the rest scored $100$ marks. Then the mean score of the students is

The average marks of $30$ students in a class was $80$. After two students left out of the class, the average marks of the remaining students was $82$. Then the average marks of the two left out students is

The average weight of a class of $14$ students is $42 \mathrm{kg}.$ On including the teacher the average increases by $400 \mathrm{g},$ then weight of teacher is

The mean of the values of $1,2,3,\dots ..n$ with respectively frequencies $x, 2x, 3x\dots , nx$ is

If a variable takes the discrete values $\alpha +4, \alpha -\frac{7}{2}, \alpha -\frac{5}{2}, \alpha -3, \alpha -2, \alpha +\frac{1}{2}, \alpha -\frac{1}{2}, \alpha +5\left(\alpha >0\right),$ then the median is

The sum of $10$ items is $12$ and the sum of their squares is $18,$ then standard deviation will be

The variance of $20$ observations is $5.$ If each observation is multiplied by $2,$ then what is the new variance of the resulting observation?

The mean and variance of $n$ values of a variable $x$ are $0$ and ${\sigma }^2,$ respectively. If the variable $y=x^2,$ then mean of $y$ is